Class-preserving automorphisms and the normalizer property for Blackburn groups

DOI10.1515/JGT.2008.068zbMath1168.16017arXivmath/0701159MaRDI QIDQ3619548

Eric Jespers, Martin Hertweck

Publication date: 8 April 2009

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701159

zbMATH Keywords

class-preserving automorphismsnormalizer propertyBlackburn groups

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Automorphisms of infinite groups (20E36) Units, groups of units (associative rings and algebras) (16U60)

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Coleman automorphisms of finite groups and their minimal normal subgroups ⋮ The influence of maximal quotient groups on the normalizer conjecture of integral group rings ⋮ On Coleman automorphisms of finite nilpotent groups by cyclic groups ⋮ Class preserving automorphisms of groups ⋮ Local-global invariants of finite and infinite groups: around Burnside from another side. ⋮ On equality of central and class preserving automorphisms of finite \(p\)-groups. ⋮ Coleman automorphisms of permutational wreath products II ⋮ The Bogomolov multiplier of rigid finite groups ⋮ Coleman automorphisms of finite groups with a self-centralizing normal subgroup ⋮ On Coleman automorphisms of wreath products of finite nilpotent groups by Abelian groups. ⋮ The normalizer property for integral group rings of holomorphs of finite groups with trivial center ⋮ The normalizer property for finite groups whose Sylow 2-subgroups are abelian ⋮ Coleman Automorphisms of Permutational Wreath Products ⋮ The Subgroup Normalizer Problem for Integral Group Rings of Some Nilpotent and Metacyclic Groups ⋮ On normal automorphisms of groups ⋮ Some results on FC-hypercentral units of integral group rings ⋮ Class-Preserving Coleman Automorphisms of Finite Groups with Prescribed Centralizers ⋮ Class-preserving Coleman automorphisms of some classes of finite groups

Cites Work

• Finite groups in which the non-normal subgroups have nontrivial intersection
• On the normalizer property for integral group rings
• Class preserving automorphisms of Blackburn groups
• On hypercentral units in integral group rings
• Class-preserving automorphisms of finite groups
• On the normalizer problem.